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Chapter 12: Cluster analysis and segmentation of customers

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Commercial applications A chain of radio-stores uses cluster analysis for identifying three different customer types with varying needs. An insurance company is using cluster analysis for classifying customers into segments like the “self confident customer”, “the price conscious customer” etc. A producer of copying machines succeeds in classifying industrial customers into “satisfied” and “non-satisfied or quarrelling” customers.

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Figure 11.1 Relatedness of multivariate methods: cluster analysis and factor analysis Cluster: X1 X2 … Xn Obs. 1 Obs. 2 Obs. 3 … Obs. i … Obs, m Classify rows Factor 1 Factor 2 Cluster 1 Cluster 2 Input-data 1 Factor:X1 X2 X3… Xj…Xn Obs. 1 Obs. 2 … Obs. m 3 Classify columns Output-data 2 4

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Dependence and Independence methods Dependence Methods: We assume that a variable (i.e. Y) depends on (are caused or determined by) other variables (X1, X2 etc.) Examples: Regression, ANOVA, Discriminant Analysis Independence Methods: We do not assume that any variable(s) is (are) caused by or determined by others. Basically, we only have X1, X2 ….Xn (but no Y) Examples: Cluster Analysis, Factor Analysis etc.

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Dependence and Independence methods Dependence Methods: The model is defined apriori (prior to survey and/or estimation) Examples: Regression, ANOVA, Discriminant Analysis Independence Methods: The model is defined aposteriori (after the survey and/or estimation has been carried out) Examples: Cluster Analysis, Factor Analysis etc. When using independence methods we let the data speak for themselves!

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Dependence method: Multiple regression Y (Sales)X1 (Price)X2 (Price Competitor)X3 (Adverting) Obs1 Obs2 Obs3 Obs4 Obs5 Obs6 Obs7 Obs8 Obs9 Obs The primary focus is on the variables!

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Independence method: Cluster analysis X1X2X3 Obs1 Obs2 Obs3 Obs4 Obs5 Obs6 Obs7 Obs8 Obs9 Obs The primary focus is on the observations! Cluster 1 Cluster 2 Cluster 3

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Cluster analysis output: A new cluster- variable with a cluster-number on each respondent X1X2X3 Cluster Obs1 Obs2 Obs3 Obs4 Obs5 Obs6 Obs7 Obs8 Obs9 Obs

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Cluster analysis: A cross-tab between the cluster- variable and background + opinions is established Cluster 1Cluster 2Cluster 3 Age %-Females Household size Opinion 1 Opinion 2 Opinion “Younger male nerds” Core-families with Traditional values “Senior-relaxers”

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Cluster profiling: (hypothetical) Buy ecological food Advertisements funny Low price important Note: Finally the clusters’ respective media-behaviour needs to be uncovered = Totally Agree Cluster 1: “Ecological shopper” Cluster 2: “Traditional shopper”

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A small example of cluster analysis Friendly (X02) Stagnant (X08) distancesCluster John Bob Cathy John-Bob John-Cathy Bob-Cathy ABAABA

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Governing principle Maximization of homogeneity within clusters and simultaneously Maximization of heterogeneity across clusters

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Figure 12.1 Overview of clustering methods Name in SPSS Between-groups linkage Within-groups linkage Nearest neighbour Furthest neighbour Centroid clustering Median clustering Ward’s method K-means cluster (Factor) HierarchicalNon-hierarchical/ Partitioning/k-means Agglomerative Divisive - Sequential threshold - Parallel threshold - Neural Networks - Optimized partitioning (8) Non-overlapping (Exclusive) Methods Overlapping Methods Non-hierarchical - Overlapping k-centroids -Overlapping k-means - Latent class techniques - Fuzzy clustering - Q-type Factor analysis (9) Linkage Methods Centroid Methods Variance Methods - Centroid (5) - Median (6) - Average - Between (1) - Within (2) - Weighted - Single - Ordinary (3) - Density - Two stage Density - Complete (4) - Ward (7) Note: Methods in italics are available In SPSS. Neural networks necessitate SPSS’ data mining tool Clementine

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Figure 12.2 Illustration of important clustering issues in Figure 12.1 Single Linkage: Minimum distance * * Complete Linkage: Maximum distance * * Average Linkage: Average distance * * * * Wards method: Minimization of within-cluster variance * * * * * ¤ * * * * ¤ Centroid method: Distance between centres * * * * * * * * * * ¤ ¤ Non overlapping Overlapping Hierarchical Non-hierarchical 1a 1b 1c 1a 1b 1b 1 1b 2 2 Agglomerative Divisive

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Euclidean distance (Default in SPSS): Other distances available in SPSS: City-Block uses of absolute differences instead of squared differences of coordinates. Moreover: Minkowski distance, Cosine distance, Chebychev distance, Pearson Correlation. * A B X Y (x 1, y 1 ) (x 2, y 2 ) y 2 -y 1 x 2 -x 1 * d = (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2

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Euclidean distance * A B X Y (1, 2) (3, 5) * d = (3-1) 2 + (5-2) 2 = 3,61

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* A * B * H * G * D * E * C * F Which two pairs of points are to be clustered first?

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Maybe A/B and D/E (depending on algorithm!) * A * B * H * G * D * E * C * F

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Quo vadis, C? * A * B * C * H * G * D * E

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Quo vadis, C? (Continued) * A * B * C * H * G * D * E

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How does one decide which cluster a “newcoming” point is to join? “Farthest neighbour” (complete linkage) “Nearest neighbour” (single linkage) “Neighbourhood centre” (average linkage) Measuring distances from point to clusters or points:

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7,010,5 9,0 8,5 9,5 12,0 11,0 * A * B * C * H * G * D * E Quo vadis, C? (Continued)

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Complete linkage Minimize longest distance from cluster to point 10,5 9,5 * A * B * C * H * G * D * E

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Average linkage Minimize average distance from cluster to point 9,0 8,5 * A * B * C * H * G * D * E

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Single linkage Minimize shortest distance from cluster to point 7,0 8,5 * A * B * C * H * G * D * E

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Single linkage: Pitfall A * * * * * * * * * B * C Chaining or Snake-like clusters All the time the closest observation is put into the existing cluster(s) Cluster formation begins A and C merge into the same cluster omitting B!

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Single linkage: Advantage Good outlier detection and removal procedure in cases with “noisy” data sets Entropy group ** * **** *** *** * Outliers * *

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Cluster analysis More potential pitfalls & problems: Do our data at all permit the use of means? Some methods (i.e. Wards) are biased toward production of clusters with approximately the same number of observations. Other methods (i. e. Centroid) require data as input that are metric scaled. So, strictly speaking it is not allowable to use this algorithm, when clustering data containing interval scales (Likert- or semantic differential scales).

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Cluster analysis: Small artificial example Note: 6 points yield 15 possible pairwise distances - [n*(n-1)]/ ,42 0,58 0,68 0,92

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Cluster analysis: Small artificial example ,42 0,58 0,68 0,92

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Cluster analysis: Small artificial example ,42 0,58 0,68 0,92

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Step 0: Each observation is treated as a separate cluster Distance Measure Dendrogram OBS 1 OBS 2 OBS 3 OBS 4 OBS 5 OBS 6 0,2 0,4 0,6 0,8 1,0 * * * * * *

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Step 1: Two observations with smallest pairwise distances are clustered Dendrogram (Continued) Cluster 1 OBS 1 OBS 2 OBS 3 OBS 4 OBS 5 OBS 6 0,2 0,4 0,6 0,8 1,0 * * * * * *

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Step 2: Two other observations with smallest distances amongst remaining points/clusters are clustered Dendrogram (Continued) Cluster 1 Cluster 2 OBS 1 OBS 2 OBS 3 OBS 4 OBS 5 OBS 6 * * * * * * 0,2 0,4 0,6 0,8 1,0

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Cluster 1 Cluster 2 Step 3: Observation 3 joins with cluster 1 Dendrogram (Continued) OBS 1 OBS 2 OBS 3 OBS 4 OBS 5 OBS 6 * * * * * * 0,2 0,4 0,6 0,8 1,0

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Dendrogram (Continued) OBS 1 OBS 2 OBS 3 OBS 4 OBS 5 OBS 6 * * * * * * “Supercluster” Step 4: Cluster 1 and 2 - from Step 3 joint into a “Supercluster” A single observation remains unclustered (Outlier) 0,2 0,4 0,6 0,8 1,0

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Textbooks in Cluster Analysis Cluster Analysis, 1981 Brian S. Everitt Cluster Analysis for Social Scientists, 1983 Maurice Lorr Cluster Analysis for Researchers, 1984 Charles Romesburg Cluster Analysis, 1984 Aldenderfer and Blashfield

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Case: Clustering of beer brands Brand profiles based om the 17 semantic differential scales Purpose: to determine the market structure in terms of similar/different brands Hypothesis: reflects the competitive structure among brands due to consumers bahaviour

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Case: Clustering of beer brands

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